Alphametics Question

Question

In the figure below, each distinct letter represents a unique digit such that the arithmetic sum holds. If the letter L represents 9, what is the digit represented by the letter T?
     TERRIBLE
  +    NUMBER
   ==========
     THIRTEEN

I know I can get the answer for this puzzle but I'm struggling to see how to solve it. Can anyone help? Thanks.

score 5 · Accepted Answer · answered Jun 03 '14 at 18:03

5

9+E = E cannot hold, unless 1 was carried from the right. This implies E+R = 10 + N. In that case 1 is carried to the left. There B+B+1 = E makes E odd. R+U = R can only hold for U = 9 and 1 from the right, but L = 9, so U = 0. E and H are distinct numbers, so H = E+1 and thus R+N = 10+I.

This is enough to significantly reduce the number of cases. We need E odd and R, E, N somewhat large. Also, H = E+1 takes up one large number. If E = 7, then H = 8, and since L = 9, we can't take R large enough for R+N > 10 to hold. If E = 3, or E = 5 and R = 7 again R+N < 10. Thus we must have E = 5, R = 8.

I'll leave it for you to finish.

answered Jun 03 '14 at 18:03

Karolis Juodelė

9,778

You are definetely correct; but look at this: $?5881295 + 30?258 = ?618?553$ The addition cannot hold, since $?$ can be only $4$ or $7$ – Riccardo Del Monte Jun 03 '14 at 19:28
@RiccardoDelMonte: Let B be 7. – Nick Matteo Jun 03 '14 at 19:48
@Kundor Thanks, got it. – Riccardo Del Monte Jun 04 '14 at 07:36

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